For example, take the number 342. It could be written out a number of different ways when spelled out fully.

Three hundred forty two

Three hundred and forty two

Three hundred and forty-two

What is the most correct form for spelling out that number in full text? What is the rule for adding (or leaving out) the and? When does one use hyphens? Does the context matter, e.g. writing out the amount on a check vs. a news article?

I was always taught, in American English, to use "and" only with compound numbers such as "three and three-quarters." Wikipedia also mentions this:

Note that in American English, many students are taught not to use the word and anywhere in the whole part of a number, so it is not used before the tens and ones. It is instead used as a verbal delimiter when dealing with compound numbers. Thus, instead of "three hundred and seventy-three", one would say "three hundred seventy-three". For details, see American and British English differences.

And as ElendilTheTall said, hyphenate numbers between twenty-one and ninety-nine as well as fractions.